While we use persistence images here, there are other potential approaches to summarising topological data analysis for use in parameter inference. For example it is possible to directly derive distances between persistence diagrams in a number of ways [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, and these could be substituted for the Euclidean distance between the vectors of persistence images that we apply. In future work we will investigate the possibility of applying a distance function on persistence diagrams in the ABC likelihood and how this influences the efficiency of the algorithm.
